If you have
dy^2/dx^2 +n^2y , this will give k^2= +/- ni , so because it isn't real is it y=Acosx + Bsinx

dy^2/dx^2 -n^2y this will give k^2= n^2, so because it is real, is it y= Ae^(nx) +Be^(-nx)

Is this correct

This is correct. You if you have complex roots to the auxiliary equation then you could write the complementary function as but if you use the fact that you will see that the conplementary function simplifies down to .
[Note. The arbitrary constants, A and B in the first and second complementary function I gave are not necessarily the same.]

(Original post by Hjyu1)
It's a triangle so all the angles add up to 180 degrees so pi radians and u already know 2 angles which are pi/6 and Alpa so you take them away from pi to get your missing angle then do sine rule

why can't you just use alpha and 1 with pi/6 and root21 /9 for the sin rule